This invention relates to peening and particularly to peening the internal surface of a hollow part and more particularly to a method for determining a peening element speed limit ratio.
Most metal parts operate in an environment which eventually leads to corrosion or the creation of stress induced cracks, thereby reducing the useful life of such parts. It is known that peening the surface of metal parts can induce compressive residual surface stresses, thereby increasing the resistance of the part to fatigue, cracking and corrosion. Numerous methods exist which relate to peening the exterior surface of metal parts. These methods, however, are not applicable to peening the internal surface of hollow parts because such methods fail to take into account the peculiar difficulties associated with peening the internal surface.
U.S. Pat. No. 2,460,657 addressed some of the distinctive characteristics associated with peening the internal surface of a hollow part. Specifically, that patent taught that vibrating the hollow part produces repeated impact between the peening elements and the internal surface of the hollow part. Additionally, U.S. Pat. No. 2,460,657 suggested that the peening elements"" vibratory motion is largely determined by their own natural frequency, but that patent does not indicate at which frequency the hollow part must vibrate in order to induce the desired residual stresses on the internal surface of a hollow part. In order to induce compressive residual stresses, the peening elements must contact the internal surface at certain velocities. The prior art, however, fails to teach one how to determine the vibration frequency and acceleration at which the hollow part must vibrate in order to cause the peening elements to contact the internal surface at such desired velocities. Specifically, the devices used to vibrate parts, such as shaker tables, typically have two controllers, namely a frequency controller and an acceleration controller to control its vibrational movement. The frequency controller sets the shaker table""s vibration frequency (xcfx89), and the acceleration controller sets the maximum sinusoidal acceleration (a). It should be understood that if the vibration frequency is known, then the acceleration can be replaced by vibration amplitude (A) because acceleration is equal to the product of the vibration amplitude and the square of the frequency (i.e., a=xcfx892A). Hence, acceleration and vibration amplitude are interchangeable, but for the purposes of this invention, the inventor shall consistently refer to acceleration rather than amplitude because the devices used to vibrate parts typically refer to acceleration rather than amplitude. It should also be understood, that as the hollow part vibrates, its instantaneous acceleration changes, but the maximum acceleration remains constant, which is hereinafter referred to as the xe2x80x9cconstant sinusoidal acceleration.xe2x80x9d
Furthermore, U.S. Pat. No. 2,460,657 indicated that the frequency of the impact between the peening elements and the hollow part should be out of step with the vibration frequency at which to vibrate the hollow part. That patent, however, did not teach how to determine or calculate the acceleration at which to vibrate the hollow part in order to produce a maximum impact rate between the peening elements and the hollow part wherein the impact rate is the rate of impact between the peening element(s) and the hollow part. Moreover, U.S. Pat. No. 2,460,657 indicated that the impact rate is determined by the peening elements own natural frequency of vibration, which is a function of the relative proportions of the peening element(s) and the hollow part, as well as their material, thereby suggesting that one could alter the proportion and material of the peening elements to change the rate of impact between the peening elements and the hollow part.
Variables other than the natural frequency of vibration and proportion and material of the peening elements may also affect the impact rate of the peening elements and the hollow part. Such other variables may include the cavity height of the hollow part and the acceleration and velocity of the hollow part. What is needed is a method for establishing a relationship between these multiple variables in order to identify the optimum frequency at which to vibrate a hollow part.
The inventors of the present invention have discovered that the rate of impact between the peening elements and an internal surface of a hollow part is a function of the vibration frequency, which is the frequency at which the hollow part vibrates, and not only a function of the peening elements"" natural frequency. Unlike U.S. Pat. No. 2,460,657, which implies that there will be repeated impact as long as the peening elements vibrate out of step with the hollow part, the inventors of the present invention have realized that there are limits at which the hollow part can vibrate and sustain repeated (i.e., cyclical) impact between the peening elements and the hollow part. xe2x80x9cRepeated impactxe2x80x9d means that the peening elements repeatedly contact the hollow part at the same frequency as the hollow part""s vibration frequency even though the repeated contact may be out of phase with the vibration frequency. The inventors of the present invention have, therefore, discovered that there is a cut-off frequency at which a hollow part can vibrate and induce repeated impact between its internal surface and the peening elements because the rate of impact becomes erratic and loses its cyclical nature as the vibration frequency deviates from the cut-off frequency.
It is an object of the present invention to provide a method for determining the cut-off frequency at which a hollow part can vibrate and maintain the repetitive nature of the impact between its internal surface and the peening elements.
It is a further object of the present invention to provide a method for determining a peening element speed limit ratio (xcex3) (hereinafter referred to as xe2x80x9cspeed limit ratioxe2x80x9d). The peening element speed limit ratio is the ratio of the velocity of the hollow part compared to the velocity of the peening element above which the rate of impact begins to become erratic and lose its cyclical nature.
It is still a further object of the present invention to utilize the speed limit ratio to calculate the acceleration at which to vibrate a hollow part when peening its internal surface. The velocity at which the peening element must impact the internal surface of the hollow part to induce certain compressive residual surface stresses is known. However, it is not known at which sinusoidal acceleration to vibrate the hollow part to cause the peening element to attain such a velocity. Developing a speed limit ratio provides an operator of a peening apparatus, such as a shaker, with the necessary sinusoidal acceleration at which to vibrate the hollow part, thereby causing the inducement of the desired compressive residual surface stresses.
According to the present invention, there is provided a method for determining the cut-off frequency at which to vibrate a hollow part when peening its surface by inserting a peening element into the hollow part, vibrating the hollow part until the peening element impacts the internal surface of the hollow part at a repetitive rate and altering the vibration frequency until the rate of impact between the peening element and internal surface is less than the vibration frequency.
An alternate method of the present invention includes using the cut-off frequency to determine the speed limit ratio for that particular hollow part. Determining the speed limit ratio includes inserting a peening element into a hollow part, vibrating the hollow part at a constant sinusoidal acceleration while varying the vibration frequency until the peening element impacts the internal surface of the hollow part at a rate equal to the vibration frequency. Upon matching the impact rate to the vibration frequency, the vibration frequency is further altered until the impact rate begins to decrease or fall below the vibration frequency. The cut-off frequency is the vibration frequency just prior to when the impact rate begins to decrease or fall below the vibration frequency. Both the velocity of the hollow part and the velocity of the peening element are determined when the hollow part vibrates at the cut-off frequency. The hollow part, thereafter, vibrates at a second constant sinusoidal acceleration, and the above process is repeated to determine the second hollow part velocity and second peening element velocity at the second cut-off frequency. The speed limit ratio (xcex3) is then calculated by dividing the difference between the first and second peening element velocities by the difference between the first and second hollow part velocities. Additional peening element velocities and hollow part velocities could also be determined by the above mentioned process to calculate the speed limit ratio.
A further embodiment of the present invention includes using the speed ratio to calculate the coefficient of restitution (xcex5) which is equal to approximately (xcex3xe2x88x921)/(xcex3+1).
A still further embodiment of the present invention includes using the speed limit ratio to calculate the acceleration of the hollow part when peening its internal surface. Specifically, a method for peening the internal surface of a hollow part includes the steps of inserting a peening element, having a diameter (d), into the cavity of the hollow part, having a cavity height (h), vibrating the hollow part at a vibration frequency equal to about       V    p        2    ⁢          (              h        -        d            )      
and an acceleration equal to or greater than about             π      ⁢              xe2x80x83            ⁢              V        p        2                    γ      ⁢              (                  h          -          d                )              ,
wherein Vp is the desired velocity of the peening element to induce the desired compressive residual stress and wherein xcex3 is the speed limit ratio. The speed limit ratio provides an operator of a peening apparatus with the relationship between the acceleration of the peening apparatus and the desired velocity of the peening element to induce the desired compressive residual stress.
The foregoing objects, features and advantages of the present invention will become more apparent in light of the following detailed description of exemplary embodiments thereof as illustrated in the accompanying drawings.